Preheat oven to 350°F.
Prepare 2 sheet pans by lining with parchment paper or silicone mats and set aside.
In a large mixing bowl, add the dry ingredients: flour, baking soda, baking powder, pumpkin spice, and salt, and whisk until combined.
In another mixing bowl, add butter and both sugars and cream until light and fluffy using a hand mixer or stand mixer.
To the butter and sugar mixture, add pumpkin puree, egg, and vanilla and stir until combined.
Combine the wet and dry ingredients together and stir until completely mixed.
Using a cookie scoop or small ice cream scoop (about 1-2 tablespoons), add scoops of cookie dough to your prepared sheet pans. Using your hand slightly wet with water, tap down the cookie dough mounds so they're a little flatter.
Bake for 15 minutes or until bottoms of cookies are slightly golden.
While the cookies are cooling, make the frosting.
In a small saucepan over medium heat, melt the butter. Add the brown sugar and reduce heat to medium low, and stir until sugar starts to dissolve.
Add the heavy cream and cook for about 2 minutes or until sugar has dissolved. Remove from heat and stir in vanilla.
Add brown sugar mixture to a large bowl with the icing sugar and whisk or use a mixer to combine until smooth. The frosting will start to thicken right away.
Spread the frosting on each cookie.
Cookies will keep in a sealed container for up to 3 days.
Makes 2 dozen cookies.